Optimal level and order of the Coiflets wavelet in the VAR time series denoise analysis

In this research, there is significance on the accuracy of estimated parameters of time series models due to noise, which can be addressed using wavelet shrinkage. Depending on the noise of the data, the wavelet with the appropriate level (the number of decomposition levels or scales used in the analysis) and order (the order N of a Coiflets wavelet is the number of vanishing moments of the wavelet function, and it also implies that the scaling function has 2 N vanishing moments) that provides the best time series model is determined. In this research, an algorithm was proposed, and the level and order optimal of the Coiflets wavelet that provides the minimum Akaike information criterion (AIC) and Bayesian information criterion (BIC) for the VAR time series model is determined with universal and minimax threshold methods with soft rule. A comparison was made between the efficiency of the proposed method and the traditional method, which relies on the level (L = 3) and order ( N = 3) for the Coiflets wavelet, and it is the default value of the MATLAB program, through studying simulation and real data. Through the research results, the efficiency of the proposed method was reached in estimating the parameters of the VAR time series model, effectively treating noise, and determining the optimal Coiflets level and order.